# What happens if I superimpose my quantum computer?

## Background

So here's a question I had. Let's say I have a quantum mechanical system which obeys the Schrodinger equation.

$$\hat H \psi = \hat T \psi + \hat V \psi$$

where $$\hat H$$ is the Hamiltonian, $$\hat T \psi$$ is the kinetic energy and $$\hat V \psi$$ is the potential. Let's say I wish to use this system as a quantum computer to perform some calculation. Now, let's I put the quantum computer itself into superposition? Now one may (reasonably) argue against this: How does one put the Hamiltonian this into superposition?

Quantum Field Theory! If I second quantize the Hamiltonian then I can have of quantum mechanical theory with superimposed particle numbers.

## Question

Now that I've superimposed the quantum computer. Is there a relation between the computation done by the original quantum computer and the super imposed quantum computer? Can someone refer me a paper where such an exploration has been done?

• When you act on a state with a Hamiltonian for a given time, you take one state and transform it into another. Now does your question refer to 1) putting this final state into a superposition? That would just require operating on the state again to put it in superposition. Or is it 2) you put the physical quantum computer itself into a superposition. That is once again putting a state into superposition, except this time your state is every atom that makes up your physical quantum computer. So you would have to expand your wave function to include all those particles. Commented Aug 15, 2023 at 7:57
• I'm talking about 2 Commented Aug 15, 2023 at 7:58
• OK, so as mentioned, in order to put your physical quantum computer into a superposition, you would have to first define the state that includes all the particles that make up your physical computer (i.e. expand your Hilbert space). Then you can just treat it as its own quantum mechanical system (you don't need quantum field theory). Does that make sense? Commented Aug 15, 2023 at 8:01
• at the end of the day, a "quantum computer" is nothing but some quantum system, with the added implicit assumption that you are particularly good at controlling it. So the state of the quantum computer will always be "in a superposition" during any computation (as any quantum state is always writable as a superposition of other states in infinitely many ways)
– glS
Commented Aug 15, 2023 at 10:06
• I'm identifying the quantum computer with the Hamiltonian rather than the ket. Commented Aug 15, 2023 at 13:04